本文關鍵詞：稀疏設計下部分函數型線性模型的估計　出處：《華東師范大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： 稀疏函數型數據 部分函數型線性模型 局部線性估計 函數型主成分分析 決定系數 收斂速度

【摘要】：過去幾十年里,函數型數據分析受到越來越多的重視,這些數據的每一個個體或試驗單元都可以近似地看成一條曲線。函數型數據可以分為稠密觀測和稀疏觀測的數據,其中稀疏函數型數據指的是稀疏、不規(guī)則的且有測量誤差的數據。函數型回歸模型是函數型數據分析中重要的研究課題,但是目前關于函數型回歸模型的研究大部分局限于完全觀測或者稠密觀測的函數型數據,而稀疏設計下的函數型回歸模型的研究還很少。本文著重研究稀疏設計下部分函數型線性模型的估計,具體將采用函數型主成分分析和非參數統(tǒng)計中的局部線性方法,得到模型中參數和斜率函數的估計,并且將線性回歸中可決系數的概念推廣到部分函數型線性模型中,給出了估計方法,然后研究了這些估計量的大樣本性質,最后通過數值模擬來說明所提出的估計方法有很好的有限樣本性質。
[Abstract]:In the past several ten years, more and more attention has been paid to the analysis of functional data. Each individual or experimental unit of these data can be regarded as a curve approximately. Functional data can be divided into dense observation and sparse observation data, where sparse function data refers to sparse data. The functional regression model is an important research topic in the functional data analysis. However, most of the researches on the functional regression model are limited to the full or dense observation of the functional data. In this paper, we focus on the estimation of partial functional linear models in sparse design. The estimation of parameter and slope function in the model will be obtained by using the local linear method of functional principal component analysis and non-parametric statistics. Furthermore, the concept of determinable coefficients in linear regression is extended to partial functional linear models, and the estimation methods are given, and the large sample properties of these estimators are studied. Finally, numerical simulation shows that the proposed estimation method has good finite sample properties.
【學位授予單位】：華東師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O212.1

【參考文獻】

相關期刊論文 前1條

1 TANG QingGuo;CHENG LongSheng;;Partial functional linear quantile regression[J];Science China(Mathematics);2014年12期

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本文編號：1355931